Distributed-element circuit: Difference between revisions

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== Circuit modelling ==

Distributed element circuits are designed with the [[distributed element model]], an alternative to the [[lumped element model]] in which the passive [[electrical element]]s of [[electrical resistance]], [[capacitance]] and [[inductance]] are assumed to be "lumped" at one point in space in a [[resistor]], [[capacitor]] or [[inductor]], respectively. The distributed element model is used when this assumption no longer holds, and thethese quantitiesproperties are considered to be distributed in space. The assumption breaks down when there is significant time for [[electromagnetic wave]]s to travel from one terminal of a component to the other; "significant", in this context, implies enough time for a noticeable [[Phase (waves)|phase]] change. The amount of phase change is dependent on the wave's [[frequency]] (and inversely dependent on [[wavelength]]). A common rule of thumb amongst engineers is to change from the lumped to the distributed model when distances involved are more than one-tenth of a wavelength (a 36° phase change). The lumped model completely fails at one-quarter wavelength (a 90° phase change), with not only the value, but the nature of the component not being as predicted. Due to this dependence on wavelength, the distributed element model is used mostly at higher frequencies; at low frequencies, distributed element components are too bulky. Distributed designs are feasible above {{nowrap|300 [[MHz]]}}, and are the technology of choice at [[microwave]] frequencies above {{nowrap|1 GHz}}.<ref>Vendelin ''et al.'', pp. 35–37</ref>

There is no clear-cut demarcation in the frequency at which these models should be used. Although the changeover is usually somewhere in the 100-to-{{nowrap|500 MHz}} range, the technological scale is also significant; miniaturised circuits can use the lumped model at a higher frequency. [[Printed circuit board]]s (PCBs) using [[through-hole technology]] are larger than equivalent designs using [[surface-mount technology]]. [[Hybrid integrated circuit]]s are smaller than PCB technologies, and [[monolithic integrated circuit]]s are smaller than both. [[Integrated circuit]]s can use lumped designs at higher frequencies than printed circuits, and this is done in some [[radio frequency]] integrated circuits. This choice is particularly significant for hand-held devices, because lumped element designs generally result in a smaller product.<ref>{{multiref|Nguyen, p. 28|Vendelin ''et al.'', pp. 35–36}}</ref>